Precalculus The Binomial Theorem Quiz: 10 Questions with Explanations

Precalculus math quiz: The Binomial Theorem – Maths PDF

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This binomial theorem quiz for Precalculus covers the binomial theorem (Common Core A-APR.C.5), with a free PDF to print.

Pick the best answer for 10 questions on binomial coefficients and expansions. Explanations name typical errors, such as forgetting to raise the coefficient of x to a power.

Precalculus · Common Core State Standards: A-APR.C.5

Binomial theorem quiz: 10 questions

Question 1

What is \(5!\)?

Question 2

What is \(C(6,2)\)?

Question 3

What is the next row of Pascal’s triangle after \(1,3,3,1\)?

Rows 0 to 4.

Question 4

How many terms does \((x+y)^{8}\) have?

Question 5

What is the coefficient of \(x\) in \((x+4)^{3}\)?

Question 6

What is the sum of the entries in row 6 of Pascal’s triangle (see the bars)?

Row 6.

Question 7

Which is the expansion of \((a-b)^{3}\)?

Question 8

The bar chart shows row 5 of Pascal’s triangle. What is the largest entry?

Row 5 entries.

Question 9

How many ways can you choose 2 of 5 books?

Question 10

Which term of \((x+2)^{5}\) contains \(x^{3}\)?

Remember

n! = n(n – 1)…(1) and 0! = 1; C(n, k) = n!/(k!(n – k)!).
Pascal’s triangle: each entry is the sum of the two above; row n sums to 2^n.
(a + b)^n = sum of C(n, k) a^(n-k) b^k for k = 0 to n.
The general term is T(k+1) = C(n, k) a^(n-k) b^k; signs alternate when b is negative.
Setting x = 1 gives the sum of the coefficients.

How to use this binomial theorem quiz

Answer each question, read the explanation that appears, and keep track of your score. A score of 8 out of 10 or more means you are ready for the test.

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